Tail Asymptotics and Estimation for Elliptical Distributions

Enkelejd Hashorva

Published 2007-08-14, updated 2008-05-15Version 3

Let (X,Y) be a bivariate elliptical random vector with associated random radius in the Gumbel max-domain of attraction. In this paper we obtain a second order asymptotic expansion of the joint survival probability P(X > x, Y> y) for x,y large. Further, based on the asymptotic bounds we discuss some aspects of the statistical modelling of joint survival probabilities and the survival conditional excess probability.